Quantum Hall Effect Transitions Research Articles

Quantum Hall effect transition in scanning gate experiments

We present systematic scanning gate studies on a two-dimensional electron gas in the regime of the quantum Hall effect (QHE). We observe the macroscopic Hall bar response as a function of the local variation of the potential landscape in order to investigate the QHE transition. At even integer filling factors, no changes can be introduced by the local perturbation, consistent with the robustness of the QHE. Between two QHE plateaus such local changes induce sharp features in the Hall resistance images. We observe two distinct $1∕B$-periodic patterns, one in the low-field part and one in the high-field part of the transition. The crossover between the patterns is smooth, with both coexisting at a characteristic filling factor. We distinguish experimentally different Hall bar responses to the perturbations, for example, in the nonlocal Hall resistance. Based on our experimental findings we draw an intuitive picture of the QHE transition as a percolation transition of edge states and their coupling at saddle points of the local potential.

Weak localisation and inter-quantum Hall effect transitions in a 2D Si/SiGe hole system

Weak localisation parameters have been determined for the 2D hole system in a strained Si/Si1−xGex heterostructure. It has been shown that by removing the effect of the lowest Landau level, the ν=2 to ν=1 quantum Hall effect transition can be considered to be a quantum Hall effect to Hall insulator transition, which can be roughly scaled using a temperature scaling exponent of κ=0.70±0.06. Previously, a similar κ was determined for the ν=1 to Hall insulator transition in this sample. The experimental value of κ is consistent with the theoretical value if the value of the temperature exponent of the phase relaxation time (p=1.55) extracted from the low field weak localisation behaviour is utilised.

Liouvillian approach to the integer quantum Hall effect transition

We present a novel approach to the localization-delocalization transition in the integer quantum Hall effect. The Hamiltonian projected onto the lowest Landau level can be written in terms of the projected density operators alone. This and the closed set of commutation relations between the projected densities leads to simple equations for the time evolution of the density operators. These equations can be used to map the problem of calculating the disorder averaged and energetically unconstrained density-density correlation function to the problem of calculating the one-particle density of states of a dynamical system with a novel action. At the self-consistent mean-field level, this approach yields normal diffusion and a finite longitudinal conductivity. While we have not been able to go beyond the saddle point approximation analytically, we show numerically that the critical localization exponent can be extracted from the energetically integrated correlation function yielding $\nu=2.33 \pm 0.05$ in excellent agreement with previous finite-size scaling studies.

On the thermal broadening of a quantum critical phase transition

The temperature dependence of an integer Quantum Hall effect transition is studied in a sample where the disorder is dominated by short-ranged potential scattering. At low temperatures the results are consistent with a ( T/ T 0) κ scaling behaviour and at higher temperatures by a linear dependence similar to that reported previously in other material systems. It is shown that the linear behaviour results from thermal broadening produced by the Fermi–Dirac distribution function and that the temperature dependence over the whole range depends both on the scaling parameter T 0 and the width of the Landau level.

Universality in an integer quantum Hall transition

An integer quantum Hall effect transition is studied in a modulation-doped $p$-SiGe sample. In contrast to most examples of such transitions the longitudinal and Hall conductivities at the critical point are close to 0.5 and 1.5 ${(e}^{2}/h),$ the theoretically expected values. This allows the extraction of a scattering parameter, describing both conductivity components, which depends exponentially on filling factor. The strong similarity of this functional form to those observed for transitions into the Hall insulating state and for the $B=0$ metal-insulator transition implies a universal quantum-critical behavior for the transitions. The observation of this behavior in the integer quantum Hall effect, for this particular sample, is attributed to the short-ranged character of the potential associated with the dominant scatterers.

Quantum Hall effect transitions in a bilayer electron system in tilted magnetic fields

The ν= 2 3 fractional quantum Hall effect (FQHE) in a wide, single quantum well subject to tilted magnetic fields makes a one-component to two-component transition induced by the in-plane component of the magnetic field. To analyze the experimental data we make a self-consistent, local-density-approximation calculation of the electronic structure of the wide quantum well in tilted magnetic fields. Our results are quantitatively consistent with the earlier experimental work on the density driven one-component to two-component FQHE transition in this system.

Localization and conductance fluctuations in the integer quantum Hall effect: Real-space renormalization-group approach

We consider the network model of the integer quantum Hall effect transition. By generalizing the real-space renormalization-group (RG) procedure for the classical percolation to the case of the quantum percolation, we derive a closed RG equation for the universal distribution of conductance of the quantum Hall sample at the transition. We find the numerical solution of the RG equation and use it to calculate the critical exponent of the localization length and the central moments of the conductance distribution. The results obtained are compared with the results of recent numerical simulations.

New Universality at the Magnetic Field Driven Insulator to Integer Quantum Hall Effect Transitions

We present a magnetotransport study of a disordered two-dimensional hole system in a strained Ge quantum well. As the magnetic field is increased, a clear transition from a low magnetic field insulator to the $\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$ quantum Hall state at the lowest density range (controlled by a gate), and to the $\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}3$ state at higher densities, is observed. We find that these transitions are characterized by a new universality: At the critical point, the diagonal and Hall resistivities are equal, within experimental uncertainty. These results are in conflict with the ``floating'' scenario suggested by Khmel'nitzkii [JETP Lett. 38, 552 (1983)] and Laughlin [Phys. Rev. Lett. 52, 2304 (1984)].